Why is the (GoF) Flyweight a structural (and not a creational) design pattern?

To my understanding, the flyweight design pattern is not so different from the factory or singleton design patterns.

It is just a factory that produces immutable (and pooled) objects. It is just a singleton that provides one instance per type (of the managed objects), instead of a global single instance.

Factory and singleton are creational patterns, so why should the flyweight be considered a structural pattern?